1. Field of the Invention
The present invention relates to the field of the digital signal processing, and more specifically, to the field of QAM modems.
2. Discussion of the Prior Art
Using the approach developed by Dominique N. Godard, “Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems”, IEEE Transaction on Communications, Vol. Com-28, No. 11, November 1980, the general problem of adaptive channel equalization can be solved without resorting to a known training sequence or to conditions of limited distortion. The criterion of equalizer adaptation is the minimization of a new class of nonconvex cost functions which are shown to characterize intersymbol interference independently of carrier phase and of the data symbol constellation used in the transmission system prior to decision directed equalization (DDE).
Thus, in the approach developed by Dominique N. Godard (Godard approach), the equalizer convergence does not require carrier recovery, so that carrier tracking can be carried out at the equalizer output in a decision-directed mode. On the other hand, in the conventional approach, the carrier tracking is done first, and the equalization is done only after the carrier tracking is achieved. Accordingly, the carrier recovery loop used in the Godard approach has latency that is lower than latency of the carrier loop used in the conventional approach. However, in a carrier loop with any low latency, one should know the direction of the error signal in order to utilize the latency properties of the carrier loop to the full extend thus minimizing the time needed for carrier tracking.
To calculate the direction of the error signal one needs to use a slicer in order to locate a plant point (corresponding to the sent signal) that is nearest to the received signal. This is a “hard decision” approach. On another hand, one can use a Viterbi decoder without using a slicer to determine the direction of the error signal. This is a soft decision approach that requires a carrier loop with even more latency than the latency of a carrier loop in the “hard decision” approach.
Even for a very good oscillator that has 1 GHz basic frequency with the maximum frequency uncertainty (or frequency offset) of up to one part per billion, the carrier tracking would result in the QAM constellation rotating at frequency of 1 Hz. However, for purposes of measurement the direction of the error signal, the constellation should be stopped completely, or stabilized. It means that the carrier tracking should be achieved with 100% accuracy in order to calculate the direction of the error signal.
To stop the rotation of the QAM constellation completely, one should design a 2-nd order carrier phase loop with the bandwidth (BW) greater than a frequency offset. Practically, in a standard commercial transmission system (like an intersystem telephone) the typical user utilizes a small antenna with a 40 GHz crystal as a source of oscillating frequency that has an uncertainly of 10 part/per million. This translates into the frequency uncertainty of (40×109×10−5)=4×104=400 kHz. Thus, one has to build a carrier loop filter with bandwidth (BW) greater than 400 kHz which requires a low latency. However, it is difficult to implement a high-rate, a low latency, and a high BW tracking loop. Indeed, for the input signal including the symbol rate of 40 Mbits/sec=4×107 symbols/sec, the ideal carrier tracking loop with a minimum latency would have no update within one clock time period. One clock period for the incoming symbol rate of 40 Mbits/sec=4×107 symbols/sec is equal to 1/(40 Mbit)=(1/40)×10−6 sec=25 nanoseconds. In a practical implementation, one would need a pipeline computation (because the whole computation might take a lot of system clocks) and would save the intermediate results at registers. However, the pipeline computation degrades the performance of the loop by reducing the loop filter's BW. Indeed, the frequency uncertainly of the carrier tracking loop for the pipeline computation is equal to the loop filter BW divided by the incoming symbol rate. In the given above example, the frequency uncertainly of the carrier tracking loop for the pipeline computation is equal to 400 kHz/4×107 symbols/sec=0.01=1%. This is a huge frequency uncertainty for one clock of pipeline computation, that only increases (though only linearly) with the number of clocks that a pipeline computation takes to perform.
What is needed is a low latency carrier tracking loop that has a large BW, as compared with the conventional large latency pipeline computation approach.